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Numerical approximation of partial differential equations

Project

Project Details

Program
Applied Mathematics and Computer Science
Field of Study
Numerical analysis, Applied Mathematics, Scientific Computing
Division
Computer, Electrical and Mathematical Sciences and Engineering
Faculty Lab Link
https://www.kaust.edu.sa/en/study/faculty/daniele-boffi

Project Description

The numerical approximation of partial differential equations is a relevant field of applied mathematics. Several projects are available at my research group, ranging from purely theoretical studied to more applied and computational tasks. Theoretical project will involve the study and analysis of the properties of the approximation of some partial differential equations. Computational projects are related to the implementation and testing of research codes for scientific computing. The areas of applications include electromagnetism, structural mechanics, fluid-dynamics, fluid-structure interactions.

About the Researcher

Daniele Boffi
Professor, Applied Mathematics and Computational Science
Computer, Electrical and Mathematical Science and Engineering Division

Affiliations

Education Profile

  • Ph.D. Mathematics, University of Pavia, 1996
  • M.S. Mathematics, University of Pavia, 1990

Research Interests

Professor Boffi's research interests are related to the numerical approximation of partial differential equations. His expertise includes the finite element methods, mixed finite elements, the numerical approximation of eigenvalue problems; his research is mainly applied to fluid-dynamics, interactions of fluids and structures, and electromagnetism.

Selected Publications

  • Boffi, Daniele and Gastaldi, Lucia, 2019, Adaptive finite element method for the Maxwell eigenvalue problem: SIAM Journal on Numerical Analysis, 57,478-494
  • Boffi, Daniele and Gastaldi, Lucia, 2017, A fictitious domain approach with distributed Lagrange multiplier for fluid-structure interactions: Numerische Mathematik, 135, 711-732
  • Boffi, Daniele, Cavallini, Nicola, and Gastaldi, Lucia, 2015, The Finite Element Immersed Boundary Method with Distributed Lagrange multiplier: SIAM Journal on Numerical Analysis, 53, 2584-2604
  • Boffi, Daniele, Brezzi, Franco, and Fortin, Michel, 2013, Mixed Finite Element Methods and Applications: Springer Series in Computational Mathematics, 44
  • Boffi, Daniele, 2010, Finite element approximation of eigenvalue problems: Acta Numerica, 19, 1-120
  • Boffi, Daniele, Costabel, Martin, Dauge, Monique, Demkowicz, Leszek, and Hiptmair, Ralf, 2011, Discrete compactness for the p-version of discrete differential forms: SIAM Journal on Numerical Analysis, 49, 135-158
  • Boffi, Daniele, Brezzi, Franco, Demkowicz, Leszek, Duran, Ricardo G., Falk, Richard S., and Fortin Michel, 2008, Mixed finite elements, compatibility conditions, and applications: Lecture Notes in Mathematics, Springer Verlag. 1939, D. Boffi, L. Gastaldi editors
  • Boffi, Daniele, Gastaldi, Lucia, Heltai, Luca, and Peskin, Charles S., (2008), On the hyper-elastic formulation of the immersed boundary method: Computer Methods in Applied Mechanics and Engineering, 197, 2210-2231
  • Boffi, Daniele, Gastaldi, Lucia, and Heltai, Luca, 2007, Numerical stability of the finite element immersed boundary method: Mathematical Models and Methods in Applied Sciences, 10, 1479-1505
  • Arnold, Douglas N., Boffi, Daniele, and Falk, Richard S., 2002, Approximation by quadrilateral finite elements: Mathematics of Computation, 71, 909-922
  • Boffi, Daniele, 2000, Fortin operator and discrete compactness for edge elements: Numerische Mathematik, 87, 229-246
  • Boffi, Daniele, Brezzi, Franco, and Gastaldi, Lucia, 2000, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form: Mathematics of Computation, 69, 121-140
  • Boffi, Daniele, Fernandes, Pablo, Gastaldi, Lucia, and Perugia, Ilaria, 1999, Computational models of electromagnetic resonators: analysis of edge element approximation: SIAM Journal on Numerical Analysis, 36, 1264-1290
  • Boffi, Daniele, 1997, Three-dimensional finite element methods for the Stokes problem: SIAM Journal on Numerical Analysis, 34, 664-670

Desired Project Deliverables

Implementation and testing of the proposed algorithms. Study and analysis of the properties of approximating schemes for partial differential equations.

Recommended Student Background

Basis Mathematical Analysis
Basic Numerical Analysis
Basic Programming
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3-6 months
Internship period
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